Invariant theory of finite groups
Fawad Hussain (U Glasgow)
Wednesday 30th May, 2012 16:00-17:00 204
Let $V$ be a finite dimensional vector space over the finite field $F_q$ with basis $e_1,\dots, e_n$. Suppose $x_1,\dots, x_n$ is the dual basis of the dual vector space $V^*$. Let $G \le GL(V)$ and consider the polynomial ring in the $n$ indeterminates $F_q[x_1,\dots, x_n]$. Invariant theory over finite fields is a branch of abstract algebra. The theory deals with those elements of $F_q[x_1,\dots, x_n]$ which do not change under the action of the group $G$. These elements form a ring structure which is called the ring of invariants of the group $G$. In this talk I will present a brief summary of my PhD thesis which is concerned with the polynomial invariants of the finite $G$.